Modeling Free Radical Graft Polymerization Of VAc From PEG And Vinyl/Divinyl Atom Transfer Radical Copolymerization With Crosslinking

Grafting and cross-linking are two important approaches for preparing novelmacromolecular materials. Modeling such processes is of great benefit for thepolymerization mechanism study and process optimization. In this thesis, themethod of moments was used in modeling the graft polymerization of vinyl acetatefrom polyethylene glycol and the vinyl/divinyl atom transfer radical copolymerizationwith cross-linking.In the first part of the thesis, a general model for the'grafting from'method wasdeveloped. A set of ordinary differential equations were derived taking into accountthe severe chain transfer reactions in the PEG/VAc system. Expressions ofpolymerization rate, molecular weight of graft-copolymer, VAc graft efficiency andPEG grafted ratio were derived using the moments.tert-Butyl peroxy-2-ethyl hexanoate was used as initiator and a weight ratio ofPEG to VAc of 1 was adopted in both simulation and experimentation. Theinfluences of polymerization temperature, initiator concentration and PEG molecularweight on the polymerization rate, copolymer MW, VAc graft efficiency and PEGgrafted ratio were analyzed using the model and were compared the experimentaldata.The model predicts the polymerization rates at various temperatures, initiatorconcentrations and PEG MWs. The simulated final conversions at high temperaturesare higher that experimental data, and the phenomenon was analyzed. The simulatedMW of graft copolymer fitted well the MW acquired by VAc graft efficiency and PEGgrafted ratio, and its value decreased with conversion at all conditions. The chaintransfer constant of VAc to PEG was estimated by correlating the model withexperimental data using a lest-square method, and the Arrhenius expression was foundto be C_PEG = 0.139exp(-11200/RT).The simulated VAc grafting efficiency was very close to 1, seemingly unaffected by temperature, initiator concentration and PEG MW. This could be explained viatwo aspects: the chain transfer rate constant of VAc to PEG is much higher than that toVAc units, and the concentration of PEG units is also much higher than VAc. ThePEG grafted ratio was also simulated and analyzed at different reaction conditions,and the C_peg expression was used. The model results agreed well with at the data ofPEG1000 and PEG 6000 systems, but deviated from PEG 6000. The discrepancywas explained.Different initial MWDs of PEG were examined using the model and it was fountthat longer PEG chains have higher probability to graft chains. The homo-PVAc andgrafted PVAc were compared using the model and were found to have the samemolecular weight distribution. The number of grafted side chains on backbone wasalso discussed at different PEG MWs. Moreover, the model was combined withsemi-batch reactor model to simulate semi-batch process. The results were alsofavorably compared with experimental data.In the second part of the thesis, the pseudo kinetic constant method was used inmodeling vinyl/divinyl cross-linking atom transfer radical polymerization. Withappropriate rate constants for the model, gel point and chain properties at gel pointwere calculated, and the effect of unequal reactivity of double bonds on gelation wasstudied.Based on the assumptions of no cyclization, equal reactivity of double bonds, andrandom distribution of cross-linkages, the gel point, total number of cross-linkages,cross-linking density and MW of primary chain were calculated and compared withFlory-Stockmayer's theory of gelation. The gel point in the vinyl/divinyl system canbe calculated via equation(?), which is derived based on Flory's theorytaking into account of ATRP characteristics. Meanwhile, the results were alsocompared with experimental data reported in literatures, and the averagecross-linkages per primary chains were calculated.The dormant distribution index and radical distribution index were also definedand calculated. At low conversion the DDI was higher than 1, indicating theexistence of poly-dormant chains. However, the RDI remained 1 prior to the gel point, and increased suddenly at the gel point, approaching infinite. Thus themono-radical assumption is valid in ATRP cross-linking system, and this is becausethe radicals are rapidly deactivated in the ATRP system.The influence of rate constants on cross-linking was also investigated. Theequilibrium rate constants for both of initiator and polymer chains had slight effect ongel point, and the influence was exerted via the consumption rate of initiator and PDIof primary chains.Different propagating rate constants for various double bonds were used to studythe effect of unequal reactivity on cross-linking. At the same reactivity ofvinyl/divinyl double bonds, increasing pendant double bond reactivity decreases thegel point, increased the total number of cross-linkages at the gel point, and alsoincreased the cross-linking density. When divinyl bond is less reactive than vinyl,the gel point was later than that of equal reactivity condition; and vice visa. Theunequal reactivity of double bonds makes theρ_bP_w change at the gel point. Whenvinyl/divinyl double bonds have the same reactivity (k_P2/k_P3=1) , the product ofρ_bP_wis close to 1.